6 ACID RAIN
Thus the concentration of HCO 3 is much greater than
that of CO 32 .^ For lower pH values, HCO 3 dominates CO 32
even more, and so CO 32 is not included in applications
related to precipitation samples (i.e., Eq. (1)).
From Eqs. (4) and (5)()()HCO3H12H K K Pco
(8)From Eqs. (3) and (8)HCOOHKKPco
K(^3) H1 2
W
()
()
(9)
where it is convenient to define
K
KKPco
K
H1 2
W
(10)
Equation (1) is now rearranged to give
H OH HCO SO NO C1
Ca Mg a K NH
343
4
()()
()
2
(^22) Ν
(11)
With the definition
Net Ions SO NO C
Ca Mg Na K NH
4
2
3
22
4
()^1
()
(12)
Eq. (11) becomes
()H OH HCO 3 (Net Ions)
(13)
With Eqs. (3), (9), and (10), Eq. (13) becomes the quadratic
equation
(H^ ^ )^2 (Net Ions)(H^ ^ ) Kw(K 1) 0 (14)
Solving for the concentration of H^ ^ gives
2(H^ ^ ) (Net Ions) [(Net Ions)^2 4K W (K 1)] 1/2 (15)
The quantity in brackets in Eq. (15) is always positive
and greater than (Net Ions), and therefore only the plus sign
in front of the bracketed term provides non-negative and
therefore physically realistic solutions for (H^ ^ ).
Equation (15) is rewritten in terms of pH as
pH log Net Ions) Net Ions)
4K K Pco 4K /
10
2
H1 2 w
6 {{(
]}}.
[(
(^052)
(16)
Equation (16) is plotted in Figure 1. If the major ions
have been measured for a precipitation sample such that
(Net Ions) can be determined with Eq. (12), then line B on
the graph allows one to read the calculated pH. Any addi-
tional ion measured, besides those listed on the right side of
Eq. (12), are simply added to Eq. (12) to make the determina-
tion of (Net Ions) just that much more accurate. If the water
sample being considered is pure water in equilibrium with
ambient carbon dioxide, then (Net Ions) 0.0 and curve B
indicates that the pH is less than or equal to 5.65.
The precipitation sample concentrations of HCO 3 , OH^ ^ ,
and H^ ^ are also shown in Figure 1, where the absolute value of
the ordinate is used to read off these concentrations. It is seen
that the HCO 3 and H^ ^ curves approach curve B. That is, at low
pH, (H^ ^ ) (Net Ions) and at high pH, (HCO 3 ) (Net Ions).
If Pco 2 0 (as it would be if one bubbled an inert
gas such as nitrogen through the precipitation sample
as the pH was being measured), then K 0 in Eq. (10),
and Eq. (16) is modified and provides the curves marked
accordingly in Figure 1. In this case, with no present
(cf. Eq. (8)), the asymptotic limit at high pH is provided
by the OH^ ^ curve.
The sensitivity of the pH prediction via Eq. (16) to the
assumed equilibrium conditions of temperature and Pco 2 is
displayed in Figure 1 by curves A to D (and of course the
Pco 2 0 curve as the extreme case). At T 25°C and Pco 2
316 10 ^6 atm, K 483. Therefore at pH 8, where
(OH^ ^ ) 1 m eq/L, (HCO 3 ) 483 m eq/L, and this procedure
explains the spacing between curves A to D and the OH^ ^ curve
in Figure 1. If the temperature is kept constant, K is propor-
tional to Pco 2. So if we double the CO 2 level (e.g., move from
curve B to C), the pH 8 intercept for HCO 3 jumps up to
(2)(483) 966. Curves A, B, C, and D (which are plots of
Eq. (16) only at high (Net Ion) values) thus graphically dem-
onstrate the sensitivity of pH to temperature and Pco 2. As a
specific example consider that with curve B and at (Net
Ions) 49, the pH 7; when Pco 2 is doubled (curve C),
the same (Net Ion) value gives pH 6.69; if the tempera-
ture is lower (curve D), then the pH 6.15.
Figure 1 also demonstrates that a bimodal pH distribution
would be expected if both high and low pH values are pres-
ent in a particular data set. For example, assume all (Net Ion)
values between 45 and 45 are equally likely. From (Net
Ion) 45 to 15, pH 0.48; from (Net Ion) 15 to 15,
pH 1.65; and from (Net Ion) 15 to 45, pH 0.48.
C001_001_r03.indd 6C001_001_r03.indd 6 11/18/2005 10:07:26 AM11/18/2005 10:07:26 AM